I'm starting developing an indie platformer game (inspired by Nintendo much underrated classic) - and this community is expert of tilesets and platformers....
What are the best tools/softwares this community uses that can be good for developing indie platformer?
Or tileset tools in general.

Also, what are the best tips for making a good platformer or mistakes analysis?
What makes platformer good or bad?

If there's one expert for tileset and map editors here, that should be K1n9_duk3.

As for a general advise, unless you are planning to make an indie studio with multiple people working on it, then don't go with over-ambitious plans for a huge platformer with many levels, tilests and features. That will take you like forever to finish what you're doing. I'm actually surprised you asked such questions since as you're a modder and graphics designer, you should be familiar with these things.

Yeah. I would also like to answer what makes platformer good or bad. That is actually a very good question. For me, a perfect indie, but retro-like classic platformer, would be, if you take the gameplay and most of the mechanics from Secret Agent, Crystal Caves and Dangerous Dave and combine them in one game. Bump up the resolution and make some nice and appealing, yet simpler tilesets. Add some more modern effects and stuff like parallax scrolling and layers. And make sure to add some new or unique mechanics that will differentiate it from the rest. Each level, if containing some unique puzzles or new graphics, is always good. Find a composer that can produce good memorable tunes. And there you go.

What makes a bad platformer. An example that comes to my mind is the Dangerous Dave remake for iphones. I really respect John Romero, but that remake was crap: unappealing graphics, bad music and sound effects, unnecessary and boring added storyline, no new levels or mechanics and only an iPhone release.